qdap: Qdadratic Discriminant Analysis by Projection

In ywwry66/QDA-by-Projection-R-Package: QDA by Projection

Qdadratic Discriminant Analysis by Projection

Description

This function runs the Quadratic Discriminant Analysis by Projection (QDAP) method.

Usage

qdap(
  x,
  y,
  xnew = NULL,
  lambda = 0,
  iter = 1,
  method = "Penalization",
  par = NULL,
  max_iter = 1000,
  optim = "codesc"
)

Arguments

x	A matrix containing the predictors of the training data.
y	A 0-1 vector containing the class labels of the training data.
xnew	A matrix containing the predictors of the test data.
lambda	The tuning parameter used for either the "Penalization" method or the "Thresholding" method. (Beta)
iter	Number of iterations to apply QDAP. If greater than 1, this will keep searching the optimal direction in the orthogonal complement of the previous optimal subspace. (Beta)
method	A method to get sparse optimal direction. "Penalization" for penalizing over the l2 norm of the optimal direction, or "Thresholding" for thresholding over each entry of the optimal direction. (Beta)
par	A vector representing the initial direction for the optimization subroutine.
max_iter	Maximum number of iterations for the optimization subroutine to run.
optim	The optimization method used towards the classification error function. "BFGS" for Broyden–Fletcher–Goldfarb–Shanno algorithm, or "codesc" for coordinate descent algorithm.

Details

This function only handles two-class classification problems. It tries to find the direction that minimizes the sample classification error under the heteroscedastic Gaussian assumption. It then projects the data onto the optimal direction, and performs 1-D regular QDA.

If not specified by the user, the initial direction for the optimization subroutine is either the LDA direction, or the direction that maximizes the ratio of two quadratic forms induced by the covariance matrices.

If the covariance matrices are singular, a tiny scalar matrix is added to them for numerical stability.

Multiple rounds of applications of QDAP is implemented (still in beta status). See the argument 'iter'.

Penalization/Thresholding is implemented to find sparse optimal direction (still in beta status). See the arguments 'lambda' and 'method'.

Value

If 'xnew' is not supplied, the return value is a list containing 'qdap_rule', 'drt' and 'conv'. If 'xnew' is supplied, in addition to these, it also contains 'class':

class	A 0-1 vector containing the predicted class label of the test data 'xnew'.
qdap_rule	The QDAP classification rule, a function that takes a vector of the same dimension as each training sample, and returns the predicted class label.
drt	a vector representing the optimal direction to project data onto.
conv	An integer code. ‘0’ indicates successful completion of the optimization method.

Examples

Iris <- iris[-which(iris$Species == "virginica"), ] # use the first two species only

## Set up training and test data
set.seed(2021)
n <- nrow(Iris)
train <- sample(1:n, n/2)
x <- Iris[train, 1:4]
y <- as.integer(Iris[train, 5] == "setosa")
xnew <- Iris[-train, 1:4]
ynew <- as.integer(Iris[-train, 5] == "setosa")

## Calculate classification error
fit <- qdap(x, y, xnew)
sum(fit$class != ynew)/length(ynew)

ywwry66/QDA-by-Projection-R-Package documentation built on Nov. 22, 2023, 2:33 a.m.